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y(x)=x⁴+3x²-6
The derivative of the function/ y(x)=x⁴+3x²-6

Derivative of y(x)=x⁴+3x²-6

Function f() - derivative -N order at the point
v

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from to

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The solution

You have entered [src] 
 4      2    
x  + 3*x  - 6
x4+3x2−6x^{4} + 3 x^{2} - 6 
d / 4      2    \
--\x  + 3*x  - 6/
dx
ddx(x4+3x2−6)\frac{d}{d x} \left(x^{4} + 3 x^{2} - 6\right)
Transform
Detail solution

  1. Differentiate x4+3x2−6x^{4} + 3 x^{2} - 6 term by term:

    1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      So, the result is: 6x6 x

    3. The derivative of the constant (−1)6\left(-1\right) 6 is zero.

    The result is: 4x3+6x4 x^{3} + 6 x

The answer is:

4x3+6x4 x^{3} + 6 x

The graph
02468-8-6-4-2-1010-2000020000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   3      
4*x  + 6*x
4x3+6x4 x^{3} + 6 x
Simplify
The second derivative [src] 
  /       2\
6*\1 + 2*x /
6⋅(2x2+1)6 \cdot \left(2 x^{2} + 1\right)
Simplify
The third derivative [src] 
24*x
24x24 x
Simplify
The graph
Derivative of y(x)=x⁴+3x²-6
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